Radio Frequency Accelerometer

ABSTRACT

Disclosure of a novel accelerometer sensor method for detecting and measuring acceleration using radio frequency (RF) oscillators. Quartz crystal oscillators (QCO) and surface acoustic wave (SAW) oscillators are known to be sensitive to acceleration or force impact events. These events cause fluctuations in the quartz crystal oscillator base natural resonant frequency. The crystalline structure of quartz crystal has a preferred direction of maximum sensitivity to acceleration. Acceleration or sudden force impact events cause fluctuations in the resonant frequency of quartz crystal and surface acoustic wave oscillators, increasing jitter and phase noise. There exists a mathematical relationship which relates these fluctuations in the natural frequency to the magnitude and direction of the accelerating source. This acceleration sensitivity can therefore be utilized to track changes in the oscillator resonant frequency referred to as jitter or phase noise to determine the magnitude of acceleration over time.

CROSS REFERENCE TO RELATED APPLICATION

This patent application claims benefit of the Aug. 21, 2018 filing date of provisional patent application No. 62/720,860 which is incorporated by reference herein.

FIELD

This disclosure relates to a novel accelerometer method.

BACKGROUND

In this embodiment advantage is taken of the properties of quartz crystal oscillators (QCO) which are known to be susceptible to acceleration or force impact events. In the current state of the art, there are predominantly three types of accelerometers: 1. Micro-Electro-Mechanical Systems (MEMS) 2. Piezoelectric 3. Piezoresistive. In this embodiment will be disclosed a novel accelerometer based on a radio frequency (RF) electronics method.

SUMMARY

RF and microwave electronic systems normally require highly accurate and stable reference oscillators and are designed to be as least sensitive to frequency disturbances as possible. These oscillator frequency disturbances are known as jitter or phase noise. Quartz crystal oscillators are known to be susceptible to increases in jitter from acceleration or force impact events. And methods have been devised to mitigate this susceptibility as much as possible. However, in this embodiment, advantage will be taken of this susceptibility to configure a highly sensitive accelerometer.

Quartz crystal oscillators are typically made from precision cut SC or AT type quartz crystals. (Most of the principles discussed here are also equally relevant to surface-acoustic-wave (SAW) oscillators). In this embodiment, in order to detect very small acceleration events, SC or AT cut oscillators would be selected to have the highest sensitivities possible to acceleration, known as g-sensitivities, where g is in reference to the earth's gravitational acceleration constant which is 9.81 meters per second squared at sea level.

BRIEF DESCRIPTIONS OF THE DRAWINGS

The invention is explained in the following descriptions of the drawings that are shown:

FIG. 1 Block diagram showing the elements in constructing the RF Mixer down-converter circuit and three methods of analysis.

FIG. 2 Depiction of RF Accelerometer using two quartz crystal oscillators with the {right arrow over (Γ)}_(max) of each oriented anti-parallel.

FIG. 3 Baseband frequency f_(Low) analyzed with Microcontroller.

FIG. 4 Diagram of frequency f_(Low) showing the Zero-point crossings of the dotted line V=0, and its Period, T₀.

FIG. 5 Phase Noise spectrum diagram of the phase noise spectrum L(f−f_(Low)).

FIG. 6 Time versus Phase Noise or Frequency monitoring setup.

FIG. 7 Angular Centripetal Acceleration/Velocity monitoring setup.

FIG. 8 Example of three RF sensors utilized for three-dimensional applications

DETAILED DESCRIPTION OF THE INVENTION

It has been shown empirically that the acceleration sensitivity of quartz crystal oscillators is a vector quantity; i.e. the shift in the quartz crystal oscillator resonant frequency is proportional to the magnitude and direction of the acceleration event. The resulting frequency is a function of acceleration and direction and can be expressed as the scalar or dot product of two vectors as shown as:

f({right arrow over (a)})=f _(o)(1+{right arrow over (Γ)}_(max) ·{right arrow over (a)})  EQUATION 1

In Equation 1, f_(o) is the quiescent natural resonant frequency of the quartz crystal oscillator without being affected by acceleration. {right arrow over (Γ)}_(max) is the acceleration sensitivity vector of the quartz crystalline structure in the direction of its maximum sensitivity. Frequency f({right arrow over (a)}) is the resonant frequency value resulting from the dot product of vector {right arrow over (a)} and the maximum acceleration sensitivity parameter of the quartz crystal oscillator, {right arrow over (Γ)}_(max). The vector dot product being defined by:

{right arrow over (Γ)}_(max) ·{right arrow over (α)}=|{right arrow over (Γ)} _(max) |*|{right arrow over (a)}|*Cos(θ)  EQUATION 2

where θ is the angle between the magnitudes of the {right arrow over (Γ)}_(max) and {right arrow over (a)} vectors.

Quartz crystal oscillators display this effect from linear dynamic acceleration caused by vibration or force impact events. This effect also displayed by constant or static acceleration, such as the earth's gravitational field, identified by the vector {right arrow over (g)}. Where we would substitute {right arrow over (g)} for {right arrow over (a)} in Equation 1. From Equation 1, we can see that in order to detect acceleration with high resolution, the AT or SC cut quartz crystal should have as high a g− sensitivity parameter value, {right arrow over (Γ)}_(max), as possible.

As seen from Equation 1, when there is zero acceleration, the f({right arrow over (a)}) value is simply the nominal value f_(o). However, when an acceleration is detected the nominal f_(o) frequency will change by an amount Δf({right arrow over (a)}) equal to:

Δf({right arrow over (a)})=f _(o)*({right arrow over (Γ)}_(max) ·{right arrow over (a)})  EQUATION 3

The quartz crystal oscillator would need to be calibrated to determine the direction and maximum value of the {right arrow over (Γ)}_(max) vector.

In an embodiment presented here, the detecting means of accelerated motion would comprise of two acceleration sensitive quartz crystal oscillators with radio frequency outputs in as high a frequency range as possible. The higher the frequencies used, the higher will be the resolution of this sensor as will be explained below. The two said quartz crystal radio frequency signals would be of approximately equal (but not exactly equal) frequencies. A radio frequency (RF) mixer would then be utilized to down-convert the two said radio frequencies to a lower baseband frequency. This baseband frequency would be the difference of the two quartz crystal oscillator inputs to the RF mixer. During an acceleration event, the said down-converted baseband frequencies will exhibit the fluctuations or jitter in the two radio frequency oscillator signals. These fluctuations would then be processed, recorded and analyzed to render a measure of the magnitude and direction of said detected acceleration event.

FIG. 1 illustrates the implementation of the embodiment by means of a radio frequency downconverter using an RF mixer 103. The RF mixer takes the frequencies F1 and F2 of QCO sources Osc_1 101 and Osc_2 102, and produces a down converted output of (F1−F2) and an up converted output of (F1+F2). In this embodiment we are interested in the downconverter (F1−F2) output signal. Therefore, a bandpass filter 104 centered on the (F1−F2) signal would be employed to filter out the said (F1+F2) output as illustrated in FIG. 1. The attenuator and amplifier circuitry 105 that follow the bandpass filter 104 could be employed to adjust the (F1−F2) signal power to an appropriate level as needed. The Osc_1 101 source could be connected to the Local Oscillator port or LO. The Osc_2 102 source would then be connected to the Radio Frequency port or RF. And the output of the RF mixer 103 is referred to as the Intermediate Frequency or IF as indicated in FIG. 1 where the unfiltered output would be the combination of frequencies of (F1−F2) and (F1+F2). The filtered f_(Low) signal could then be analyzed by any of three methods using an Oscilloscope 106, a Spectrum Analyzer 107, or by means of a Microcontroller 108.

To enhance the sensitivity of this sensor, the two oscillator sources would be aligned such that the maximum sensitivity vectors ({right arrow over (Γ)}_(max1) 202 of oscillator Osc_1 201 and {right arrow over (Γ)}_(max2) 204 of Osc_2 203, oscillator) are anti-parallel to each other as illustrated in FIG. 2. Therefore, if an acceleration event is in the direction of the {right arrow over (Γ)}_(max1) 202 for the Osc_1 201 oscillator, the nominal frequency of F1 will be positively increased with the acceleration, while frequency F2 of Osc_2 203, will correspondingly decrease.

Therefore, the difference of the signals (F1−F2) out of the RF mixer 103 will be f_(Low), given by:

f _(Low) =f({right arrow over (a)})₁ −f({right arrow over (a)})₂=(f _(o1) +Δf({right arrow over (a)})₁)−(f _(o2) −Δf({right arrow over (a)})₂)=(f _(o1) −f _(o2))+f _(o1)*({right arrow over (Γ)}_(max1) ·{right arrow over (a)})+f _(o2)*({right arrow over (Γ)}_(max2) ·{right arrow over (a)})  EQUATION 4

Where Δf({right arrow over (a)})₂ will be negative with respect to Δf({right arrow over (a)})₁, since the {right arrow over (Γ)}_(max) vectors of the sources are configured to be in opposite directions. With the crystalline structure of the two oscillators aligned anti-parallel, the {right arrow over (Γ)}_(max) of each is pointing in the opposite direction making the final frequency f_(Low) equal to the difference in the base resonant frequencies (f_(o1)−f_(o2)), plus the addition of the frequency changes in sources due to the accelerating event. The total change in frequency due to the acceleration would therefore be the sum of Δf({right arrow over (a)})₁ and Δf({right arrow over (a)})₂ given by:

Δf({right arrow over (a)})_(Total) =f _(o1)*({right arrow over (Γ)}_(max1) ·{right arrow over (a)})+f _(o2)*({right arrow over (Γ)}_(max2) ·{right arrow over (a)})  EQUATION 5

In order to further enhance the sensitivity and increase the resolution of this radio frequency accelerometer sensor, higher values of the original nominal values (f_(o1) and f_(o2)) of the oscillators would be used to increase the resulting change in Δf({right arrow over (a)})_(Total), as given in EQUATION 5.

After the two source signals are down converted to the baseband frequency, f_(Low), this embodiment proposes a possible method of analyzing this signal which correlates to the frequency variations caused from an acceleration event. The Digital Signal Processing method can be utilized by taking the f_(Low) signal and applying it to a Microcontroller, as illustrated in FIG. 3.

The resulting down converted f_(Low) frequency will display jitter as illustrated in FIG. 4 where T_(o) represents the period of frequency f_(Low). This jitter results in a characteristic power spectrum pattern known as phase noise as depicted in FIG. 5 (Where center frequency f_(C)=f_(Low) in FIG. 5). The frequency, f_(Low), would then be processed and analyzed by the Microcontroller to determine the zero to zero-point crossings of f_(Low).

This type of analysis would be advantageous since in the case of frequency versus time analysis, if we are attempting to track the frequency vs time sequence of the f_(Low) frequency fluctuations, there is an inherent limitation as indicated by a principle related to the Heisenberg Uncertainty principle called the Heisenberg-Gabor Uncertainty Principle. The Heisenberg-Gabor Uncertainty Principle states that it is not possible to monitor both the exact frequency shifts and the exact time the shifts occur with arbitrary accuracy. Given mathematically by:

Δω×Δt>=½,  EQUATION 6

Applying this principle to this application, the uncertainty in the time period measurement, ΔT_(o), is ΔT_(o)=Δt. The uncertainty in the f_(Low) frequency shifts measurement is related to angular frequency Δω by, Δω/2π=Δf_(Low), which would result with as follows:

Δω×Δt=Δf _(Low)×2π×ΔT _(o)>=½, or:

Δf _(Low) ×ΔT _(o)>=¼π  EQUATION 7

To mitigate this limitation, rather than track frequency variations over time, the time period of the baseband f_(Low) signal, T_(o), would be monitored for cycle to cycle variations. With today's high-speed Microcontroller, unprecedented resolution and sensitivity to very small accelerations could be attained compared to currently available accelerometers. The high-speed Microcontroller would be utilized to extract very small frequency fluctuations by monitoring the changes in the period T_(o) of frequency f_(Low). The practical limiting factor in recording the time the period T_(o) measurement would be made and the duration of the period, T_(o), would be +/− the time resolution of the Microcontroller clock itself. Which would depend on the sampling rate of the Microcontroller. Which with today's Microcontroller would be very high. The fluctuations in T_(o) as depicted in FIG. 4 by the shaded area, could therefore be accurately measured and correlated to acceleration events over time.

Another analysis method would be as follows. One could track phase noise detected by the down-converted baseband frequency, as explained previously, using a spectrum analyzer setup for phase-noise measurements. In this method, after the output frequencies of the oscillator sources have been down converted and low pass filtered, if the IF output (F1−F2) is at a relatively high frequency level, a conventional Spectrum Analyzer 603 could be used, See FIG. 6. In using a Spectrum Analyzer 603, one could measure the phase noise of the (F1−F2) signal. As depicted in FIG. 4, there would be jitter on the baseband (F1−F2) signal with a nominal period T_(o) resulting in phase variations along the dotted line of the voltage threshold, V_(th) level crossings. There always exists some jitter on all QCO signals causing some nominal phase noise even with zero acceleration. Jitter in the nominal f_(o) frequency would increase at the moment of an acceleration or force impact event. A Spectrum Analyzer based measurement system controlled by a Personal Computer 602, could be designed with automated programming 601 to automate tracking and recording of the signal phase noise over time. Statistical methods could be utilized to monitor and compare the phase noise of a signal during quiescent periods with times and correlate the phase noise measured to the acceleration or force impact events.

Alternatively, one could utilize an Oscilloscope and again automate measurements by programming control of the oscilloscope through the Personal Computer to monitor and record frequency over time, see FIG. 6. Choice of which setup to use would depend on which configuration would be the most efficient, cost effective and produce the most accurate tracking of the effects of acceleration over time.

This embodiment has been shown to be applicable to measurements of linear acceleration. One could as well take the measurements of acceleration and apply mathematical integration to calculate linear velocity. The embodiment could also be utilized for measurements of angular acceleration or velocity as illustrated in FIG. 7. The paired quartz crystal oscillators are placed on a spinning circular platform along the radius of the circle platform. The two oscillator sources are placed in the anti-parallel configuration as presented in FIG. 2. However as shown in FIG. 7, the two QCOs would be configured right next to each other so as to place each of them at the same radius distance. In this configuration the oscillators will pick up the centripetal acceleration {right arrow over (a)}_(c) of the spinning platform with angular velocity ω, with the centripetal acceleration given by:

{right arrow over (a)} _(c) =v ² /r  EQUATION 8

And each QCO would pick up the same tangential velocity, V, at the point where they are attached on the spinning platform.

A single said stand-alone RF accelerometer sensor of this embodiment can be used in the detection of acceleration along any arbitrary direction. Or three sensors could also be utilized for three-dimensional applications with, for example, the main axis of highest acceleration sensitivity {right arrow over (Γ)}_(max) of each of three RF accelerometer sensors aligned along the direction of the three-orthogonal axis as depicted in FIG. 8. The three RF sensor g-sensitivities could be aligned with {right arrow over (Γ)}_(x) along the North-South, {right arrow over (Γ)}_(y) along the East-West and {right arrow over (Γ)}_(z) along the negative z-direction of earth's −g local static acceleration value.

As mentioned previously, this RF Accelerometer sensor can detect the earth's static gravitational acceleration, {right arrow over (g)}. Variations in {right arrow over (g)} over the earth's surface could therefore be measured. This embodiment could therefore find application in geological subsurface analysis and exploration. This embodiment could also be applied as a seismometer to detect seismic activity using for example the three-dimensional arrangement shown in FIG. 8. 

What is claimed:
 1. A Radio Frequency (RF) accelerometer sensor method utilizing the susceptibility of quartz crystal oscillators (QCO) and surface acoustic wave (SAW) oscillators to acceleration, for the purpose of sensing and measuring acceleration. The natural resonant frequencies of quartz crystal oscillators are subject to fluctuations according to an empirical mathematical relationship. In said mathematical relationship, the maximum acceleration sensitivity vector and the vector of the accelerating source, when multiplied as a vector dot product, renders the magnitude of the frequency variation of the QCO or SAW oscillator.
 2. Said method in claim 1 uses QCO's which individually are configured to have the highest g sensitivity values possible.
 3. Said method in claim 1 requires utilizing quartz crystal (or SAW) oscillators that operate at the highest resonant radio frequencies possible to enhance resolution.
 4. To enhance the resolution or sensitivity to acceleration events of said method in claim 1, the sensor would be configured to utilize a pair of quartz crystal oscillators.
 5. Said accelerometer sensor in claim 4 would configure a pair of QCO's such that the directions of maximum sensitivity vectors are anti-parallel so as to enhance sensor sensitivity to acceleration. With the sensitivity vectors of the two QCO's being anti-parallel, the change in the QCO pointing in the direction of the acceleration would cause a positive change to the QCO's natural frequency. The other QCO being in the opposite direction to the acceleration would cause a negative change in its natural frequency. Performing a subtraction of the negative changing frequency from the positive one yields a total frequency change higher than that of a single QCO oscillator.
 6. Said accelerometer sensor in claim 5 can also be applied to measure rotational acceleration and velocity as well as linear acceleration.
 7. The linear acceleration measurements of the sensor of claim 4 can also be mathematically integrated to yield linear velocity as well. 